TRAJECTORY OPTIMIZATION FOR LOW-THRUST MULTIPLE ASTEROIDS RENDEZVOUS MISSION

A mission designed to rendezvous with a dozen asteroids in the Main-Belt with low-thrust propulsion within a preset duration is investigated. Indirect methods with homotopic approaches and switching moments detection methods are implemented to optimize the low-thrust trajectories. Optimization of low-thrust trajectories between two asteroids is derived first. With fixed initial and terminating moments, the utilization of homotopic approach provides a fast method to obtain an approximation even with random guesses. To further improve the efficiency to optimize low-thrust transfers between low-inclination low-eccentricity orbits, an effective method is proposed to help providing initial guesses. To optimize the low-thrust trajectory to rendezvous with a dozen asteroids in whole, the conditions for optimality are concluded which are used to build the shooting function. The method to split the trajectory into several segments and solve them sequentially is applied first. Then the results obtained in the last step are used to provide initial guesses to optimize the low-thrust transfers in whole. The method to use them is proposed with some basic derivations. Finally the homotopic form is removed and the bang-off-bang control is directly solved. Numerical examples where three sequences containing a dozen asteroids are optimized demonstrates the validity of these methods.